a) A stellar-mass black hole has the mass of the sun (1.9 x 1033 grams), and a r
ID: 1545309 • Letter: A
Question
a) A stellar-mass black hole has the mass of the sun (1.9 x 1033 grams), and a radius of 2.9 kilometers. i) What would be the tidal acceleration across a human at a distance of 100 kilometers? ii) Would a human be spaghettified? b) A supermassive black hole has 100 million times the mass of the sun and an event horizon radius of 295 million kilometers. What would be the tidal acceleration across a 2 metre tall human at a distance of 100 kilometers from the event horizon of the supermassive black hole? Would the astronaut be spaghettified?
Explanation / Answer
formula for accleration is
a=GMd/R^3
= a = 2 x (6.67 x 10^-8) x(1.9 x 10^33)x 200 / (1.0 x 10^7)^3
=50,700,000 cm/sec^2
Yes, this is equal to 50,700,000/979 = 51,700 times the acceleration of
gravity, and a human would be pulled apart and 'spaghettified'
------------------------------------------------------------------------------------------------
(b)
a = 2 x (6.67 x 10^-8) x(1.9 x 10^41)x 200 / (2.95 x 10^13)^3
= 0.00020 cm/sec^2
The supermassive black hole, because the tidal force is far less than what a
human normally experiences on the surface of Earth. That raises the question that as a
space traveler, you could find yourself
trapped by a supermassive black hole unless you
knew exactly what its size was before hand.
You would have no physical sensation of
having crossed over the black hole's Event Horizon before it was too late.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.